Sequencing problems may be common across multiple industries. By way of example and not by way of limitation, a stock cutting problem may be common in the composite aircraft industry. A stock cutting problem may be posed as how one may arrange individual pattern shapes on a material bed for cutting in a manner minimizing the amount of wasted material. By way of further example and not by way of limitation, a resource constrained project scheduling problem may be common in aircraft manufacturing and overhaul operations. A resource constrained project scheduling problem may be posed as how one may order operations to be performed in a manner to maximize utilization of resources and minimize overall duration.
Sequencing problems are generally categorized, within the theory of computation, as NP-Complete, meaning that sequencing problems are members of a large family of especially difficult problems where the time required to find a solution grows exponentially with the size of the problem. Without use of specialized methods, the time required to find good solutions to sequencing problems is proportional to N! The symbol N! may be known as “n-factorial”. N!=n*(n−1)*(n−2) . . . *2*1) where N may be the number of items to be sequenced.
By way of example and not by way of limitation, potential uses of this method may include                use to find optimized solutions to conventional sequencing problems in design, manufacturing, maintenance, and transportation, where the objective is to optimize the sequence of operations, actions, events, or other occurrences ordered in time, including traveling salesman problem, line balancing problems, scheduling manufacturing and maintenance, data transmissions in a communications network, and similar problems.        use to find optimized solutions to conventional sequencing problems in design, manufacturing, maintenance, and transportation, where the objective is to optimize the placement of objects, components, or other physical objects ordered in space, including the stock cutting problem, pattern layout problem, circuit board design, communications network design, and similar problems.        use to optimize the results of a decision process by optimizing the sequence of discrete decisions, including use of this method to optimize the sequence of decisions within classical “branch-and-bound” decision trees, commonly used within Operations Research.        use to optimize the results of a physical process by optimizing the sequence of discrete actions, including synthesis of novel organic compounds that arise through sequences of heating, cooling, hydration, dehydration, exposure to ultraviolet light, exposure to electrical discharge, and other physical conditions.        use to find optimized solutions to any problem within the family of NP-Complete problems, by rendering said problems as sequencing problems, using this method to find an optimized solution, including NP-complete problems described in Computer Science literature.        use to optimize the sequence of atoms within a molecular structure, including the sequence of atoms within DNA or RNA, the sequence of atoms within proteins, the sequence of atoms within polymers, or the sequence of layers within a crystal lattice.        
While algorithms may have been developed for some particular sequencing problems, general purpose methods for solution of sequencing problems remain elusive. Genetic Algorithms have proven useful in many computational problems. While Genetic Algorithms may be useful for general sequencing problems, they may have limited value for large problems, problems that have large-scale structure, and other circumstances.
There is a need for a system and method for optimizing a sequential arrangement of items that may be substantially generally applied to a wide variety and range of sequencing problems.